Heavy flavor physics may provide many details of the Standard Model, such as information of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements, the intrinsic structure of the strong interaction, possible evidences of new physics beyond the Standard Model, and so on. Investigation of heavy \(b\)  or \(c\)  mesons or baryons appeals much interest both in experiments and theory. There are many research works on the \(\Lambda _c\)  baryon in the past years. In experiments, data of the process \(\Lambda _c\rightarrow pK^-\pi ^+\)  has been obtained and improved in fairly good accuracy. Early in 2013 the Belle Collaboration at KEKB measured the first model independent branching ratio \(\mbox{Br}{(\Lambda _c\rightarrow pK^-\pi ^+)}=(6.84\pm 0.24^{+0.21}_{-0.27})\%\)[1]}. This measurement improved the precision of the absolute branching ratios of other decay modes of the \(\Lambda _c\)  baryon. Next in 2015 the BESIII Collaboration reported the first absolute measurement of the branching ratio of the semileptonic decay process \(\Lambda _c \rightarrow \Lambda e^+ \nu _e\) , \(\mbox{Br}{(\Lambda _c\rightarrow \Lambda e^+\nu _e)}=(3.63\pm 0.38(sta)\pm 0.20(sys))\%\)[2]}. Later in 2016, the BESIII Collaboration gives the improvement of the \(\Lambda _c\)  decay modes, including the process \(\Lambda _c \rightarrow p K^-\pi ^+\) , \(\mbox{Br}{(\Lambda _c\rightarrow pK^-\pi ^+)}=(5.84\pm 0.27\pm 0.23)\%\)[3]}. Many theoretical analysis have been devoted to the topic, including the covariant quark model[4]}, [5]}, the light-cone QCD sum rules[6]}, [7]}, [8]}, the SU(3) flavor symmety[9]}, the relativistic quark model[10]}, and other models[11]}, [12]}.
